C. E. Campbell

Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J(1)-J(2)-J(3) model

We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 J1-J2-J3 model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength J1≡1, we find four magnetically ordered phases in the parameter window J2,J3∈[0,1], namely, the Neel, striped, and Neel-II collinear AFM phases, plus a spiral phase. The Neel-II phase appears as a stable GS phase in the classical version of the model only for values J3<0. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) (Jc12,Jc13)=(0.51±0.01,0.69±0.01) between the Neel, striped, and QP phases; (b) (Jc22,Jc23)=(0.65±0.02,0.55±0.01) between the striped, spiral, and QP phases; and (c) (Jc32,Jc33)=(0.69±0.01,0.12±0.01) between the spiral, Neel-II, and QP phases.

Correlated density matrix theory of normal quantum fluids

Abstract A variational description of the normal phase of a strongly interacting N-boson fluid at finite temperature is formulated in terms of trial density matrices designed to incorporate the essential dynamical and statistical correlations. The approach followed is a natural extension, to the noncondensed phase, of the familiar Jastrow-Feenberg variational approximation of correlated-basis functions theory, which has provided a firm foundation for microscopic calculations of the properties of liquid 4He at zero temperature. The N-body density matrix elements of the homogeneous fluid are represented in the general form W(R, R′) = J−1φ(R) Q(R, R′) φ(R′) involving a normalization integral J = ∫dR φ2(R) Q(R, R), where R denotes a point in the configuration space of the system. This form is specialized by assuming φ(R) to be a wave function of Jastrow type, i.e., a product of two-body dynamical correlation functions f(r) = exp [ u(r) 2 ] , and taking Q(R, R′) to be a permanent part of two-body statistical functions Γ(r). It is in the latter assumption, which tailors the treatment to the normal phase, that the present approach departs from earlier work within variational density matrix theory, which focuses instead on the condensed or superfluid phase. The internal energy, the spatial distribution functions, and the one-body density matrix of the system may all be constructed from variational derivatives of the normalization integral J (or of a generalized version of J ), carried out with respect to the dynamical or statistical correlation functions entering the theory. The required normalization integrals are susceptible to analysis in terms of generalized Ursell-Mayer cluster diagrams; systematic diagrammatic resummations based on the hypernetted-chain (HNC) classification scheme are then performed following standard prescriptions. Neglecting elementary diagrams, one arrives at explicit expressions for the indicated equilibrium properties as functionals of the trial correlations u(r) and Γ(r). Making use of the replica technique, it is possible to treat the entropy by the same procedures. With appropriate simplifications to facilitate the associated analytic continuation, one arrives at an entropy expression equivalent to that of a system of noninteracting bosons occupying single-particle momentum states k with an occupation number ncc(k) determined by the solution of the HNC equations arising in the treatment of the internal energy. In the culminating step of the formal development, an explicit functional expression for the Helmholtz free energy is assembled from the results obtained for the internal energy and entropy, and the Gibbs-Delbruck-Moliere minimum principle is invoked. Functional variation of the free energy with respect to the correlation function u(r) and a renormalized statistical correlation function Γcc(r) leads to coupled Euler-Lagrange equations which are the analogs of the paired-phonon equation for a Bose superfluid at zero temperature and of the Feynman eigenvalue equation determining the elementary excitations of the superfluid phase. The solutions provide the ingredients of a condition that signals the occurrence of a Bose-Einstein transition in the correlated system. Specific attention is given to the inclusion of phonon effects in the ansatz for the correlated density matrix, a necessary refinement for quantitative treatment of the gas-liquid spinodal line and critical point. An analogous correlated density matrix formalism is developed for the normal phase of a strongly interacting fluid of spinless fermions at finite temperature. In the limiting case of zero temperature, this approach reproduces the well-known Fermi hypernetted-chain theory of the Jastrow-correlated Fermi sea.

Magnetic order in a spin- 1 2 interpolating square-triangle Heisenberg antiferromagnet

Using the coupled cluster method (CCM) we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called J1?J2? model, defined on an anisotropic two-dimensional lattice. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1>0) bonds between nearest neighbors and competing (J2?>0) bonds between next-nearest neighbors across only one of the diagonals of each square plaquette, the same diagonal in every square. Considered on an equivalent triangular-lattice geometry the model may be regarded as having two sorts of nearest-neighbor bonds, with J2???J1 bonds along parallel chains and J1 bonds providing an interchain coupling. Each triangular plaquette thus contains two J1 bonds and one J2? bond. Hence, the model interpolates between a spin-half HAF on the square lattice at one extreme (?=0) and a set of decoupled spin-half chains at the other (???), with the spin-half HAF on the triangular lattice in between at ?=1. We use a N�el state, a helical state, and a collinear stripe-ordered state as separate starting model states for the CCM calculations that we carry out to high orders of approximation (up to eighth order, n=8, in the localized subsystem set of approximations, LSUBn). The interplay between quantum fluctuations, magnetic frustration, and varying dimensionality leads to an interesting quantum phase diagram. We find strong evidence that quantum fluctuations favor a weakly first-order or possibly second-order transition from N�el order to a helical state at a first critical point at ?c1=0.80�0.01 by contrast with the corresponding second-order transition between the equivalent classical states at ?cl=0.5. We also find strong evidence for a second critical point at ?c2=1.8�0.4 where a first-order transition occurs, this time from the helical phase to a collinear stripe-ordered phase. This latter result provides quantitative verification of a recent qualitative prediction of and Starykh and Balents [Phys. Rev. Lett. 98, 077205 (2007)] based on a renormalization group analysis of the J1?J2? model that did not, however, evaluate the corresponding critical point.

The effect of anisotropy on the ground-state magnetic ordering of the spin-1 quantum J1XXZ–J2XXZ model on the square lattice

We study the zero-temperature phase diagram of the J XXZ 1 -J XXZ 2 Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour (J1 ≡ 1) and next-nearest-neighbour (J2 > 0) bonds. The two bonds have the same XXZ -type anisotropy in spin space. The effects on the quasiclassical Neel-ordered and collinear stripe-ordered states of varying the anisotropy parameterare investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- 1 particles studied previously, no intermediate disordered phase between the Neel and collinear stripe phases, for any value of the frustration J2/J1, for either the z-aligned ( �> 1) or xy -planar-aligned (0 �< 1) states, is predicted here. The quantum phase transition is determined as first order for all values of J2/J1

Frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 J_1?J_2?J_3 antiferromagnet with J_2 =J_3 = ?J_1 on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We presentresults for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N�eel antiferromagnetic (AFM) phase for ? ?_{c}_{2} ? 0.60, and a paramagnetic PVBC phase for ?_{c}_{1} < ? < ?_{c}}_{2}. . The transition at ?_{c}_{2} appears to be of first-order type, while that at ?_{c}_{1} is continuous. Since the N�eel and PVBC phases break differentsymmetries our results favor the deconfinement scenario for the transition at ?_{c}_{1}..

Magnetic order on a frustrated spin- 1 2 Heisenberg antiferromagnet on the Union Jack lattice

We use the coupled cluster method (CCM) to study the zero-temperature phase diagram of a two-dimensional frustrated spin-half antiferromagnet, the so-called Union Jack model. It is defined on a square lattice such that all nearest-neighbor pairs are connected by bonds with a strength J1>0, but only half the next-nearest-neighbor pairs are connected by bonds with a strength J2≡κJ1>0. The bonds are arranged such that on the 2×2 unit cell they form the pattern of the Union Jack flag. Alternating sites on the square lattice are thus four-connected and eight-connected. We find strong evidence for a first phase transition between a Neel antiferromagnetic phase and a canted ferrimagnetic phase at a critical coupling κc1=0.66±0.02. The transition is an interesting one, at which the energy and its first derivative seem continuous, thus providing a typical scenario of a second-order transition (just as in the classical case for the model), although a weakly first-order transition cannot be excluded. By contrast, the average on-site magnetization approaches a nonzero value Mc1=0.195±0.005 on both sides of the transition, which is more typical of a first-order transition. The slope, dM/dκ, of the order parameter curve as a function of the coupling strength κ, also appears to be continuous, or very nearly so, at the critical point κc1, thereby providing further evidence of the subtle nature of the transition between the Neel and canted phases. Our CCM calculations provide strong evidence that the canted ferrimagnetic phase becomes unstable at large values of κ, and hence we have also used the CCM with a model collinear semistripe-ordered ferrimagnetic state in which alternating rows (and columns) are ferromagnetically and antiferromagnetically ordered, and in which the spins connected by J2 bonds are antiparallel to one another. We find tentative evidence, based on the relative energies of the two states, for a second zero-temperature phase transition between the canted and semistripe-ordered ferrimagnetic states at a large value of the coupling parameter around κc2≈125±5. This prediction, however, is based on an extrapolation of the CCM results for the canted state into regimes where the solutions have already become unstable and the CCM equations based on the canted state at any level of approximation beyond the lowest have no solutions. Our prediction for κc2 is hence less reliable than that for κc1. Nevertheless, if this second transition at κc2 does exist, our results clearly indicate it to be of first-order type.

Phase diagram of a frustrated spin-½ J1-J2 XXZ model on the honeycomb lattice

We study the zero-temperature (

Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J(1)-J(2) model

T = 0

QUANTUM STICKING, SCATTERING, AND TRANSMISSION OF 4HE ATOMS FROM SUPERFLUID 4HE SURFACES

) ground-state (GS) properties of a frustrated spin-half

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

J_{1}^{XXZ}